Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
2072 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C34×C19⋊C3 | C3 | semidirect |
| 2. C3×#13095315 | C3 | semidirect |
| 3. C3×#13095314 | C3 | semidirect |
| 4. C3×#13095313 | C3 | semidirect |
| 5. #17987418 | C3 | semidirect |
| 6. (C3×C19⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 7. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 14. C3×#10587025 | C32 | semidirect |
| 16. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 22. C3×C19×3−1+2 | C32 | semidirect |
| 23. C3×C19×H(3,𝔽3) | C32 | semidirect |
| 30. C33×C19 | H(3,𝔽3) | semidirect |
| 46. C32×C19⋊C3 | H(3,𝔽3) | semidirect |
| 63. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 88. C3×C19⋊C3 | AΣL(1,𝔽27) | semidirect |
| 99. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 102. C3×H(3,𝔽3) | C3×C19⋊C3 | semidirect |
| 136. C33 | C32⋊(C19⋊C3) | semidirect |
| 150. C19 | #10624730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C19⋊C3 | 3 |
| C3×#13095315 | 3 |
| C3×#13095314 | 3 |
| C3×#13095313 | 3 |
| #17987418 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| #10624730 | 19 |